I have a Gateway computer that is about 8 months old. It uses an Intel E6300 1.83Ghz C2D processor. I don't use the onboard video, but rather an nVidia 7600 PCIe card I added myself. The model of the computer is GT5238E and it has 1GB of RAM. The only thing I use this computer for is playing MS FSX. After playing for 8 months the lack of detail and performance is ticking me off. The best fps I can get is around 20fps with all the settings at low to medium. My main question is whether just upgrading the video card to an 8600 or 8800 would solve all my gaming woes with FSX or if the processor is providing a significant bottleneck too?

The GFX card could always use an improvement, but the one you have is sufficient for decent fps rates. What I would recommend is buying a few more sticks of RAM to install for your system. 1GB is actually quite slow these days. If you could push that to 8GB, it would see a marked improvement, but this can also be solved by the upgrade to 8600/8800 too. (I would go for the 8800).

Also, your core processor is a little on the slower side too. It might be possible to overclock the one you have, but I would probably recommend an upgrade here too. Individual components for PC's these days are generally much cheaper.